LMFDB - Embedded newform 889.2.a.c.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [889,2,Mod(1,889)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(889, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("889.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 889 = 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	889.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.09870073969$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} + \cdots + 1 $ x^16 - 2x^15 - 20x^14 + 38x^13 + 155x^12 - 275x^11 - 593x^10 + 957x^9 + 1177x^8 - 1655x^7 - 1150x^6 + 1279x^5 + 474x^4 - 280x^3 - 83x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.191617$ of defining polynomial
Character	$\chi$	$=$	889.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.191617 q^{2} -2.32908 q^{3} -1.96328 q^{4} +3.92161 q^{5} -0.446291 q^{6} -1.00000 q^{7} -0.759431 q^{8} +2.42462 q^{9} +0.751445 q^{10} -5.26691 q^{11} +4.57265 q^{12} +6.07655 q^{13} -0.191617 q^{14} -9.13374 q^{15} +3.78105 q^{16} -4.12322 q^{17} +0.464598 q^{18} +0.0374083 q^{19} -7.69922 q^{20} +2.32908 q^{21} -1.00923 q^{22} -3.57588 q^{23} +1.76878 q^{24} +10.3790 q^{25} +1.16437 q^{26} +1.34010 q^{27} +1.96328 q^{28} -2.19905 q^{29} -1.75018 q^{30} +4.14885 q^{31} +2.24337 q^{32} +12.2671 q^{33} -0.790078 q^{34} -3.92161 q^{35} -4.76022 q^{36} -9.31219 q^{37} +0.00716804 q^{38} -14.1528 q^{39} -2.97819 q^{40} -9.48327 q^{41} +0.446291 q^{42} -11.4342 q^{43} +10.3404 q^{44} +9.50842 q^{45} -0.685199 q^{46} -3.87164 q^{47} -8.80637 q^{48} +1.00000 q^{49} +1.98879 q^{50} +9.60333 q^{51} -11.9300 q^{52} -9.97552 q^{53} +0.256785 q^{54} -20.6547 q^{55} +0.759431 q^{56} -0.0871269 q^{57} -0.421374 q^{58} -9.91129 q^{59} +17.9321 q^{60} -0.382013 q^{61} +0.794988 q^{62} -2.42462 q^{63} -7.13223 q^{64} +23.8298 q^{65} +2.35057 q^{66} +4.40596 q^{67} +8.09505 q^{68} +8.32853 q^{69} -0.751445 q^{70} -10.3123 q^{71} -1.84133 q^{72} -3.37816 q^{73} -1.78437 q^{74} -24.1735 q^{75} -0.0734430 q^{76} +5.26691 q^{77} -2.71191 q^{78} +9.73339 q^{79} +14.8278 q^{80} -10.3951 q^{81} -1.81715 q^{82} +16.5257 q^{83} -4.57265 q^{84} -16.1697 q^{85} -2.19098 q^{86} +5.12177 q^{87} +3.99985 q^{88} -2.53028 q^{89} +1.82197 q^{90} -6.07655 q^{91} +7.02047 q^{92} -9.66301 q^{93} -0.741870 q^{94} +0.146700 q^{95} -5.22500 q^{96} -5.85331 q^{97} +0.191617 q^{98} -12.7703 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{3} + 12 q^{4} - 9 q^{5} - 12 q^{6} - 16 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} - 22 q^{11} - 10 q^{12} - 4 q^{13} + 2 q^{14} - 14 q^{15} + 12 q^{16} - 18 q^{17} - 5 q^{18} - 15 q^{19}+ \cdots - 73 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^3 + 12 * q^4 - 9 * q^5 - 12 * q^6 - 16 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 - 22 * q^11 - 10 * q^12 - 4 * q^13 + 2 * q^14 - 14 * q^15 + 12 * q^16 - 18 * q^17 - 5 * q^18 - 15 * q^19 - 40 * q^20 + 4 * q^21 - 11 * q^22 - 5 * q^23 - 26 * q^24 + 15 * q^25 - 24 * q^26 - 10 * q^27 - 12 * q^28 - 12 * q^29 + 3 * q^30 - 32 * q^31 - 9 * q^32 - 10 * q^33 - 14 * q^34 + 9 * q^35 + 10 * q^36 - 2 * q^37 + 3 * q^38 - 41 * q^39 - 14 * q^40 - 45 * q^41 + 12 * q^42 - 3 * q^43 - 54 * q^44 - 22 * q^45 - 49 * q^47 + 10 * q^48 + 16 * q^49 - 6 * q^50 - 12 * q^51 + 38 * q^52 + 16 * q^53 - 67 * q^54 + 7 * q^55 + 6 * q^56 + 8 * q^57 + 16 * q^58 - 35 * q^59 + 56 * q^60 - 11 * q^61 + 17 * q^62 - 14 * q^63 - 2 * q^64 + 14 * q^65 + 86 * q^66 + 17 * q^67 - 71 * q^68 - 17 * q^69 + 2 * q^70 - 81 * q^71 + 13 * q^72 - 15 * q^73 + 13 * q^74 - 48 * q^75 + 14 * q^76 + 22 * q^77 - 10 * q^78 - 34 * q^79 - 33 * q^80 + 40 * q^81 - 14 * q^82 - 39 * q^83 + 10 * q^84 - 17 * q^85 + 36 * q^86 + 7 * q^87 + 61 * q^88 - 32 * q^89 + 79 * q^90 + 4 * q^91 + 37 * q^92 + 27 * q^93 + 13 * q^94 - 33 * q^95 - 55 * q^96 - 4 * q^97 - 2 * q^98 - 73 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.191617	0.135493	0.0677467	−	0.997703i	$-0.478419\pi$
$2$	0.191617	0.135493	0.0677467	+	0.997703i	$0.478419\pi$
$3$	−2.32908	−1.34470	−0.672348	−	0.740235i	$-0.734714\pi$
$3$	−2.32908	−1.34470	−0.672348	+	0.740235i	$0.734714\pi$
$4$	−1.96328	−0.981642
$5$	3.92161	1.75380	0.876898	−	0.480677i	$-0.159609\pi$
$5$	3.92161	1.75380	0.876898	+	0.480677i	$0.159609\pi$
$6$	−0.446291	−0.182197
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.759431	−0.268499
$9$	2.42462	0.808208
$10$	0.751445	0.237628
$11$	−5.26691	−1.58803	−0.794016	−	0.607897i	$-0.792014\pi$
$11$	−5.26691	−1.58803	−0.794016	+	0.607897i	$0.792014\pi$
$12$	4.57265	1.32001
$13$	6.07655	1.68533	0.842665	−	0.538438i	$-0.180985\pi$
$13$	6.07655	1.68533	0.842665	+	0.538438i	$0.180985\pi$
$14$	−0.191617	−0.0512117
$15$	−9.13374	−2.35832
$16$	3.78105	0.945262
$17$	−4.12322	−1.00003	−0.500014	−	0.866017i	$-0.666672\pi$
$17$	−4.12322	−1.00003	−0.500014	+	0.866017i	$0.666672\pi$
$18$	0.464598	0.109507
$19$	0.0374083	0.00858204	0.00429102	−	0.999991i	$-0.498634\pi$
$19$	0.0374083	0.00858204	0.00429102	+	0.999991i	$0.498634\pi$
$20$	−7.69922	−1.72160
$21$	2.32908	0.508247
$22$	−1.00923	−0.215168
$23$	−3.57588	−0.745623	−0.372812	−	0.927907i	$-0.621606\pi$
$23$	−3.57588	−0.745623	−0.372812	+	0.927907i	$0.621606\pi$
$24$	1.76878	0.361050
$25$	10.3790	2.07580
$26$	1.16437	0.228351
$27$	1.34010	0.257902
$28$	1.96328	0.371026
$29$	−2.19905	−0.408353	−0.204177	−	0.978934i	$-0.565452\pi$
$29$	−2.19905	−0.408353	−0.204177	+	0.978934i	$0.565452\pi$
$30$	−1.75018	−0.319537
$31$	4.14885	0.745155	0.372577	−	0.928001i	$-0.378474\pi$
$31$	4.14885	0.745155	0.372577	+	0.928001i	$0.378474\pi$
$32$	2.24337	0.396576
$33$	12.2671	2.13542
$34$	−0.790078	−0.135497
$35$	−3.92161	−0.662872
$36$	−4.76022	−0.793371
$37$	−9.31219	−1.53091	−0.765457	−	0.643487i	$-0.777487\pi$
$37$	−9.31219	−1.53091	−0.765457	+	0.643487i	$0.777487\pi$
$38$	0.00716804	0.00116281
$39$	−14.1528	−2.26626
$40$	−2.97819	−0.470893
$41$	−9.48327	−1.48104	−0.740519	−	0.672035i	$-0.765420\pi$
$41$	−9.48327	−1.48104	−0.740519	+	0.672035i	$0.765420\pi$
$42$	0.446291	0.0688641
$43$	−11.4342	−1.74370	−0.871850	−	0.489774i	$-0.837079\pi$
$43$	−11.4342	−1.74370	−0.871850	+	0.489774i	$0.837079\pi$
$44$	10.3404	1.55888
$45$	9.50842	1.41743
$46$	−0.685199	−0.101027
$47$	−3.87164	−0.564737	−0.282368	−	0.959306i	$-0.591120\pi$
$47$	−3.87164	−0.564737	−0.282368	+	0.959306i	$0.591120\pi$
$48$	−8.80637	−1.27109
$49$	1.00000	0.142857
$50$	1.98879	0.281257
$51$	9.60333	1.34473
$52$	−11.9300	−1.65439
$53$	−9.97552	−1.37024	−0.685122	−	0.728429i	$-0.740251\pi$
$53$	−9.97552	−1.37024	−0.685122	+	0.728429i	$0.740251\pi$
$54$	0.256785	0.0349440
$55$	−20.6547	−2.78508
$56$	0.759431	0.101483
$57$	−0.0871269	−0.0115402
$58$	−0.421374	−0.0553292
$59$	−9.91129	−1.29034	−0.645170	−	0.764039i	$-0.723214\pi$
$59$	−9.91129	−1.29034	−0.645170	+	0.764039i	$0.723214\pi$
$60$	17.9321	2.31503
$61$	−0.382013	−0.0489118	−0.0244559	−	0.999701i	$-0.507785\pi$
$61$	−0.382013	−0.0489118	−0.0244559	+	0.999701i	$0.507785\pi$
$62$	0.794988	0.100964
$63$	−2.42462	−0.305474
$64$	−7.13223	−0.891528
$65$	23.8298	2.95573
$66$	2.35057	0.289335
$67$	4.40596	0.538273	0.269137	−	0.963102i	$-0.413262\pi$
$67$	4.40596	0.538273	0.269137	+	0.963102i	$0.413262\pi$
$68$	8.09505	0.981669
$69$	8.32853	1.00264
$70$	−0.751445	−0.0898148
$71$	−10.3123	−1.22385	−0.611925	−	0.790916i	$-0.709604\pi$
$71$	−10.3123	−1.22385	−0.611925	+	0.790916i	$0.709604\pi$
$72$	−1.84133	−0.217003
$73$	−3.37816	−0.395383	−0.197692	−	0.980264i	$-0.563344\pi$
$73$	−3.37816	−0.395383	−0.197692	+	0.980264i	$0.563344\pi$
$74$	−1.78437	−0.207429
$75$	−24.1735	−2.79132
$76$	−0.0734430	−0.00842449
$77$	5.26691	0.600220
$78$	−2.71191	−0.307063
$79$	9.73339	1.09509	0.547546	−	0.836776i	$-0.315562\pi$
$79$	9.73339	1.09509	0.547546	+	0.836776i	$0.315562\pi$
$80$	14.8278	1.65780
$81$	−10.3951	−1.15501
$82$	−1.81715	−0.200671
$83$	16.5257	1.81393	0.906964	−	0.421209i	$-0.138394\pi$
$83$	16.5257	1.81393	0.906964	+	0.421209i	$0.138394\pi$
$84$	−4.57265	−0.498917
$85$	−16.1697	−1.75385
$86$	−2.19098	−0.236260
$87$	5.12177	0.549111
$88$	3.99985	0.426386
$89$	−2.53028	−0.268209	−0.134105	−	0.990967i	$-0.542816\pi$
$89$	−2.53028	−0.268209	−0.134105	+	0.990967i	$0.542816\pi$
$90$	1.82197	0.192053
$91$	−6.07655	−0.636995
$92$	7.02047	0.731935
$93$	−9.66301	−1.00201
$94$	−0.741870	−0.0765181
$95$	0.146700	0.0150512
$96$	−5.22500	−0.533274
$97$	−5.85331	−0.594314	−0.297157	−	0.954829i	$-0.596038\pi$
$97$	−5.85331	−0.594314	−0.297157	+	0.954829i	$0.596038\pi$
$98$	0.191617	0.0193562
$99$	−12.7703	−1.28346
$100$	−20.3769	−2.03769
$101$	−1.78412	−0.177527	−0.0887633	−	0.996053i	$-0.528291\pi$
$101$	−1.78412	−0.177527	−0.0887633	+	0.996053i	$0.528291\pi$
$102$	1.84016	0.182203
$103$	−8.17058	−0.805071	−0.402536	−	0.915404i	$-0.631871\pi$
$103$	−8.17058	−0.805071	−0.402536	+	0.915404i	$0.631871\pi$
$104$	−4.61471	−0.452510
$105$	9.13374	0.891362
$106$	−1.91148	−0.185659
$107$	3.22757	0.312021	0.156010	−	0.987755i	$-0.450137\pi$
$107$	3.22757	0.312021	0.156010	+	0.987755i	$0.450137\pi$
$108$	−2.63099	−0.253167
$109$	16.9092	1.61961	0.809805	−	0.586700i	$-0.199573\pi$
$109$	16.9092	1.61961	0.809805	+	0.586700i	$0.199573\pi$
$110$	−3.95779	−0.377360
$111$	21.6889	2.05861
$112$	−3.78105	−0.357275
$113$	5.58588	0.525476	0.262738	−	0.964867i	$-0.415375\pi$
$113$	5.58588	0.525476	0.262738	+	0.964867i	$0.415375\pi$
$114$	−0.0166950	−0.00156363
$115$	−14.0232	−1.30767
$116$	4.31736	0.400857
$117$	14.7333	1.36210
$118$	−1.89917	−0.174833
$119$	4.12322	0.377975
$120$	6.93644	0.633208
$121$	16.7403	1.52185
$122$	−0.0732001	−0.00662722
$123$	22.0873	1.99155
$124$	−8.14536	−0.731475
$125$	21.0943	1.88673
$126$	−0.464598	−0.0413897
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−5.85340	−0.517372
$129$	26.6312	2.34475
$130$	4.56619	0.400481
$131$	−15.7005	−1.37176	−0.685879	−	0.727716i	$-0.740582\pi$
$131$	−15.7005	−1.37176	−0.685879	+	0.727716i	$0.740582\pi$
$132$	−24.0837	−2.09622
$133$	−0.0374083	−0.00324371
$134$	0.844254	0.0729325
$135$	5.25533	0.452307
$136$	3.13130	0.268507
$137$	7.97414	0.681277	0.340639	−	0.940194i	$-0.389357\pi$
$137$	7.97414	0.681277	0.340639	+	0.940194i	$0.389357\pi$
$138$	1.59588	0.135851
$139$	−3.40873	−0.289125	−0.144562	−	0.989496i	$-0.546177\pi$
$139$	−3.40873	−0.289125	−0.144562	+	0.989496i	$0.546177\pi$
$140$	7.69922	0.650703
$141$	9.01737	0.759399
$142$	−1.97601	−0.165823
$143$	−32.0046	−2.67636
$144$	9.16762	0.763968
$145$	−8.62381	−0.716169
$146$	−0.647310	−0.0535718
$147$	−2.32908	−0.192099
$148$	18.2825	1.50281
$149$	−2.34920	−0.192454	−0.0962271	−	0.995359i	$-0.530678\pi$
$149$	−2.34920	−0.192454	−0.0962271	+	0.995359i	$0.530678\pi$
$150$	−4.63205	−0.378205
$151$	−3.42902	−0.279050	−0.139525	−	0.990219i	$-0.544558\pi$
$151$	−3.42902	−0.279050	−0.139525	+	0.990219i	$0.544558\pi$
$152$	−0.0284090	−0.00230427
$153$	−9.99727	−0.808231
$154$	1.00923	0.0813258
$155$	16.2701	1.30685
$156$	27.7859	2.22465
$157$	−19.8947	−1.58777	−0.793886	−	0.608067i	$-0.791945\pi$
$157$	−19.8947	−1.58777	−0.793886	+	0.608067i	$0.791945\pi$
$158$	1.86508	0.148378
$159$	23.2338	1.84256
$160$	8.79762	0.695513
$161$	3.57588	0.281819
$162$	−1.99187	−0.156496
$163$	6.68481	0.523595	0.261797	−	0.965123i	$-0.415685\pi$
$163$	6.68481	0.523595	0.261797	+	0.965123i	$0.415685\pi$
$164$	18.6183	1.45385
$165$	48.1066	3.74509
$166$	3.16659	0.245775
$167$	16.0276	1.24025	0.620126	−	0.784502i	$-0.287082\pi$
$167$	16.0276	1.24025	0.620126	+	0.784502i	$0.287082\pi$
$168$	−1.76878	−0.136464
$169$	23.9244	1.84034
$170$	−3.09837	−0.237634
$171$	0.0907010	0.00693608
$172$	22.4486	1.71169
$173$	−14.8583	−1.12965	−0.564827	−	0.825209i	$-0.691057\pi$
$173$	−14.8583	−1.12965	−0.564827	+	0.825209i	$0.691057\pi$
$174$	0.981416	0.0744009
$175$	−10.3790	−0.784578
$176$	−19.9144	−1.50111
$177$	23.0842	1.73512
$178$	−0.484844	−0.0363406
$179$	−10.4016	−0.777456	−0.388728	−	0.921353i	$-0.627085\pi$
$179$	−10.4016	−0.777456	−0.388728	+	0.921353i	$0.627085\pi$
$180$	−18.6677	−1.39141
$181$	−6.10810	−0.454011	−0.227006	−	0.973893i	$-0.572894\pi$
$181$	−6.10810	−0.454011	−0.227006	+	0.973893i	$0.572894\pi$
$182$	−1.16437	−0.0863086
$183$	0.889740	0.0657715
$184$	2.71564	0.200199
$185$	−36.5187	−2.68491
$186$	−1.85159	−0.135765
$187$	21.7166	1.58808
$188$	7.60113	0.554369
$189$	−1.34010	−0.0974777
$190$	0.0281102	0.00203933
$191$	8.67944	0.628022	0.314011	−	0.949419i	$-0.398327\pi$
$191$	8.67944	0.628022	0.314011	+	0.949419i	$0.398327\pi$
$192$	16.6115	1.19883
$193$	−4.28438	−0.308396	−0.154198	−	0.988040i	$-0.549279\pi$
$193$	−4.28438	−0.308396	−0.154198	+	0.988040i	$0.549279\pi$
$194$	−1.12159	−0.0805255
$195$	−55.5016	−3.97455
$196$	−1.96328	−0.140235
$197$	20.8740	1.48721	0.743606	−	0.668618i	$-0.233114\pi$
$197$	20.8740	1.48721	0.743606	+	0.668618i	$0.233114\pi$
$198$	−2.44700	−0.173900
$199$	23.3191	1.65305	0.826525	−	0.562900i	$-0.190314\pi$
$199$	23.3191	1.65305	0.826525	+	0.562900i	$0.190314\pi$
$200$	−7.88213	−0.557350
$201$	−10.2618	−0.723814
$202$	−0.341867	−0.0240537
$203$	2.19905	0.154343
$204$	−18.8540	−1.32005
$205$	−37.1897	−2.59744
$206$	−1.56562	−0.109082
$207$	−8.67018	−0.602619
$208$	22.9757	1.59308
$209$	−0.197026	−0.0136286
$210$	1.75018	0.120774
$211$	−17.2768	−1.18938	−0.594691	−	0.803954i	$-0.702726\pi$
$211$	−17.2768	−1.18938	−0.594691	+	0.803954i	$0.702726\pi$
$212$	19.5848	1.34509
$213$	24.0183	1.64571
$214$	0.618456	0.0422768
$215$	−44.8404	−3.05809
$216$	−1.01771	−0.0692465
$217$	−4.14885	−0.281642
$218$	3.24009	0.219446
$219$	7.86800	0.531670
$220$	40.5511	2.73395
$221$	−25.0550	−1.68538
$222$	4.15594	0.278929
$223$	26.8248	1.79632	0.898162	−	0.439665i	$-0.144903\pi$
$223$	26.8248	1.79632	0.898162	+	0.439665i	$0.144903\pi$
$224$	−2.24337	−0.149892
$225$	25.1652	1.67768
$226$	1.07035	0.0711985
$227$	18.2819	1.21341	0.606707	−	0.794925i	$-0.292490\pi$
$227$	18.2819	1.21341	0.606707	+	0.794925i	$0.292490\pi$
$228$	0.171055	0.0113284
$229$	4.27326	0.282385	0.141192	−	0.989982i	$-0.454906\pi$
$229$	4.27326	0.282385	0.141192	+	0.989982i	$0.454906\pi$
$230$	−2.68708	−0.177181
$231$	−12.2671	−0.807113
$232$	1.67003	0.109643
$233$	−0.982041	−0.0643357	−0.0321678	−	0.999482i	$-0.510241\pi$
$233$	−0.982041	−0.0643357	−0.0321678	+	0.999482i	$0.510241\pi$
$234$	2.82315	0.184555
$235$	−15.1830	−0.990433
$236$	19.4587	1.26665
$237$	−22.6699	−1.47257
$238$	0.790078	0.0512131
$239$	−8.88724	−0.574868	−0.287434	−	0.957800i	$-0.592802\pi$
$239$	−8.88724	−0.574868	−0.287434	+	0.957800i	$0.592802\pi$
$240$	−34.5351	−2.22923
$241$	−27.4668	−1.76929	−0.884646	−	0.466264i	$-0.845600\pi$
$241$	−27.4668	−1.76929	−0.884646	+	0.466264i	$0.845600\pi$
$242$	3.20772	0.206200
$243$	20.1907	1.29523
$244$	0.750000	0.0480138
$245$	3.92161	0.250542
$246$	4.23230	0.269841
$247$	0.227313	0.0144636
$248$	−3.15076	−0.200074
$249$	−38.4896	−2.43918
$250$	4.04202	0.255640
$251$	−7.65870	−0.483413	−0.241706	−	0.970349i	$-0.577707\pi$
$251$	−7.65870	−0.483413	−0.241706	+	0.970349i	$0.577707\pi$
$252$	4.76022	0.299866
$253$	18.8339	1.18407
$254$	−0.191617	−0.0120231
$255$	37.6605	2.35839
$256$	13.1428	0.821428
$257$	−19.3455	−1.20674	−0.603369	−	0.797462i	$-0.706176\pi$
$257$	−19.3455	−1.20674	−0.603369	+	0.797462i	$0.706176\pi$
$258$	5.10298	0.317697
$259$	9.31219	0.578631
$260$	−46.7847	−2.90146
$261$	−5.33187	−0.330035
$262$	−3.00847	−0.185864
$263$	12.7413	0.785660	0.392830	−	0.919611i	$-0.371496\pi$
$263$	12.7413	0.785660	0.392830	+	0.919611i	$0.371496\pi$
$264$	−9.31598	−0.573359
$265$	−39.1201	−2.40313
$266$	−0.00716804	−0.000439501 0
$267$	5.89323	0.360660
$268$	−8.65014	−0.528392
$269$	9.02960	0.550545	0.275272	−	0.961366i	$-0.411232\pi$
$269$	9.02960	0.550545	0.275272	+	0.961366i	$0.411232\pi$
$270$	1.00701	0.0612846
$271$	16.6046	1.00866	0.504328	−	0.863512i	$-0.331740\pi$
$271$	16.6046	1.00866	0.504328	+	0.863512i	$0.331740\pi$
$272$	−15.5901	−0.945289
$273$	14.1528	0.856565
$274$	1.52798	0.0923085
$275$	−54.6652	−3.29644
$276$	−16.3513	−0.984230
$277$	−7.79112	−0.468123	−0.234061	−	0.972222i	$-0.575202\pi$
$277$	−7.79112	−0.468123	−0.234061	+	0.972222i	$0.575202\pi$
$278$	−0.653169	−0.0391745
$279$	10.0594	0.602240
$280$	2.97819	0.177981
$281$	−8.94643	−0.533700	−0.266850	−	0.963738i	$-0.585983\pi$
$281$	−8.94643	−0.533700	−0.266850	+	0.963738i	$0.585983\pi$
$282$	1.72788	0.102894
$283$	−11.5107	−0.684243	−0.342121	−	0.939656i	$-0.611145\pi$
$283$	−11.5107	−0.684243	−0.342121	+	0.939656i	$0.611145\pi$
$284$	20.2460	1.20138
$285$	−0.341678	−0.0202392
$286$	−6.13261	−0.362629
$287$	9.48327	0.559780
$288$	5.43933	0.320516
$289$	0.000967701 0	5.69236e−5 0
$290$	−1.65246	−0.0970361
$291$	13.6328	0.799171
$292$	6.63228	0.388125
$293$	−4.41505	−0.257930	−0.128965	−	0.991649i	$-0.541166\pi$
$293$	−4.41505	−0.257930	−0.128965	+	0.991649i	$0.541166\pi$
$294$	−0.446291	−0.0260282
$295$	−38.8682	−2.26299
$296$	7.07196	0.411049
$297$	−7.05817	−0.409557
$298$	−0.450146	−0.0260763
$299$	−21.7290	−1.25662
$300$	47.4595	2.74007
$301$	11.4342	0.659056
$302$	−0.657057	−0.0378094
$303$	4.15536	0.238719
$304$	0.141442	0.00811228
$305$	−1.49811	−0.0857813
$306$	−1.91564	−0.109510
$307$	4.82910	0.275611	0.137806	−	0.990459i	$-0.455995\pi$
$307$	4.82910	0.275611	0.137806	+	0.990459i	$0.455995\pi$
$308$	−10.3404	−0.589201
$309$	19.0300	1.08258
$310$	3.11763	0.177069
$311$	−15.7618	−0.893772	−0.446886	−	0.894591i	$-0.647467\pi$
$311$	−15.7618	−0.893772	−0.446886	+	0.894591i	$0.647467\pi$
$312$	10.7480	0.608488
$313$	13.2573	0.749349	0.374675	−	0.927156i	$-0.377754\pi$
$313$	13.2573	0.749349	0.374675	+	0.927156i	$0.377754\pi$
$314$	−3.81216	−0.215132
$315$	−9.50842	−0.535739
$316$	−19.1094	−1.07499
$317$	5.19102	0.291557	0.145778	−	0.989317i	$-0.453431\pi$
$317$	5.19102	0.291557	0.145778	+	0.989317i	$0.453431\pi$
$318$	4.45198	0.249655
$319$	11.5822	0.648479
$320$	−27.9698	−1.56356
$321$	−7.51727	−0.419573
$322$	0.685199	0.0381846
$323$	−0.154243	−0.00858229
$324$	20.4085	1.13380
$325$	63.0684	3.49841
$326$	1.28092	0.0709436
$327$	−39.3830	−2.17788
$328$	7.20189	0.397658
$329$	3.87164	0.213450
$330$	9.21802	0.507435
$331$	−11.1884	−0.614969	−0.307485	−	0.951553i	$-0.599487\pi$
$331$	−11.1884	−0.614969	−0.307485	+	0.951553i	$0.599487\pi$
$332$	−32.4446	−1.78063
$333$	−22.5786	−1.23730
$334$	3.07115	0.168046
$335$	17.2784	0.944022
$336$	8.80637	0.480427
$337$	17.1501	0.934223	0.467111	−	0.884198i	$-0.345295\pi$
$337$	17.1501	0.934223	0.467111	+	0.884198i	$0.345295\pi$
$338$	4.58431	0.249354
$339$	−13.0100	−0.706605
$340$	31.7456	1.72165
$341$	−21.8516	−1.18333
$342$	0.0173798	0.000939792 0
$343$	−1.00000	−0.0539949
$344$	8.68348	0.468182
$345$	32.6612	1.75842
$346$	−2.84709	−0.153061
$347$	0.0256912	0.00137917	0.000689587	−	1.00000i	$-0.499780\pi$
$347$	0.0256912	0.00137917	0.000689587		1.00000i	$0.499780\pi$
$348$	−10.0555	−0.539031
$349$	23.9479	1.28190	0.640950	−	0.767583i	$-0.278541\pi$
$349$	23.9479	1.28190	0.640950	+	0.767583i	$0.278541\pi$
$350$	−1.98879	−0.106305
$351$	8.14316	0.434650
$352$	−11.8156	−0.629775
$353$	−6.33830	−0.337354	−0.168677	−	0.985671i	$-0.553949\pi$
$353$	−6.33830	−0.337354	−0.168677	+	0.985671i	$0.553949\pi$
$354$	4.42332	0.235097
$355$	−40.4409	−2.14638
$356$	4.96766	0.263285
$357$	−9.60333	−0.508262
$358$	−1.99313	−0.105340
$359$	−10.9811	−0.579563	−0.289781	−	0.957093i	$-0.593583\pi$
$359$	−10.9811	−0.579563	−0.289781	+	0.957093i	$0.593583\pi$
$360$	−7.22099	−0.380579
$361$	−18.9986	−0.999926
$362$	−1.17041	−0.0615155
$363$	−38.9896	−2.04642
$364$	11.9300	0.625301
$365$	−13.2478	−0.693421
$366$	0.170489	0.00891160
$367$	21.0669	1.09968	0.549840	−	0.835270i	$-0.314689\pi$
$367$	21.0669	1.09968	0.549840	+	0.835270i	$0.314689\pi$
$368$	−13.5206	−0.704809
$369$	−22.9934	−1.19699
$370$	−6.99759	−0.363787
$371$	9.97552	0.517903
$372$	18.9712	0.983612
$373$	10.6031	0.549009	0.274505	−	0.961586i	$-0.411486\pi$
$373$	10.6031	0.549009	0.274505	+	0.961586i	$0.411486\pi$
$374$	4.16127	0.215174
$375$	−49.1304	−2.53708
$376$	2.94024	0.151631
$377$	−13.3626	−0.688211
$378$	−0.256785	−0.0132076
$379$	−5.57679	−0.286460	−0.143230	−	0.989689i	$-0.545749\pi$
$379$	−5.57679	−0.286460	−0.143230	+	0.989689i	$0.545749\pi$
$380$	−0.288015	−0.0147748
$381$	2.32908	0.119322
$382$	1.66312	0.0850928
$383$	19.7345	1.00838	0.504192	−	0.863592i	$-0.331791\pi$
$383$	19.7345	1.00838	0.504192	+	0.863592i	$0.331791\pi$
$384$	13.6330	0.695708
$385$	20.6547	1.05266
$386$	−0.820958	−0.0417857
$387$	−27.7236	−1.40927
$388$	11.4917	0.583403
$389$	16.1098	0.816799	0.408399	−	0.912803i	$-0.366087\pi$
$389$	16.1098	0.816799	0.408399	+	0.912803i	$0.366087\pi$
$390$	−10.6350	−0.538525
$391$	14.7442	0.745645
$392$	−0.759431	−0.0383570
$393$	36.5677	1.84460
$394$	3.99981	0.201507
$395$	38.1705	1.92057
$396$	25.0717	1.25990
$397$	−6.80662	−0.341614	−0.170807	−	0.985304i	$-0.554638\pi$
$397$	−6.80662	−0.341614	−0.170807	+	0.985304i	$0.554638\pi$
$398$	4.46833	0.223977
$399$	0.0871269	0.00436180
$400$	39.2435	1.96217
$401$	−17.1989	−0.858873	−0.429437	−	0.903097i	$-0.641288\pi$
$401$	−17.1989	−0.858873	−0.429437	+	0.903097i	$0.641288\pi$
$402$	−1.96634	−0.0980720
$403$	25.2107	1.25583
$404$	3.50273	0.174267
$405$	−40.7654	−2.02565
$406$	0.421374	0.0209125
$407$	49.0464	2.43114
$408$	−7.29306	−0.361060
$409$	3.13066	0.154801	0.0774005	−	0.997000i	$-0.475338\pi$
$409$	3.13066	0.154801	0.0774005	+	0.997000i	$0.475338\pi$
$410$	−7.12615	−0.351936
$411$	−18.5724	−0.916111
$412$	16.0412	0.790291
$413$	9.91129	0.487703
$414$	−1.66135	−0.0816509
$415$	64.8071	3.18126
$416$	13.6320	0.668362
$417$	7.93922	0.388785
$418$	−0.0377534	−0.00184658
$419$	18.8437	0.920576	0.460288	−	0.887770i	$-0.347746\pi$
$419$	18.8437	0.920576	0.460288	+	0.887770i	$0.347746\pi$
$420$	−17.9321	−0.874998
$421$	−13.1531	−0.641045	−0.320523	−	0.947241i	$-0.603859\pi$
$421$	−13.1531	−0.641045	−0.320523	+	0.947241i	$0.603859\pi$
$422$	−3.31052	−0.161153
$423$	−9.38727	−0.456425
$424$	7.57572	0.367909
$425$	−42.7949	−2.07586
$426$	4.60230	0.222982
$427$	0.382013	0.0184869
$428$	−6.33663	−0.306293
$429$	74.5414	3.59889
$430$	−8.59217	−0.414351
$431$	−38.5459	−1.85669	−0.928346	−	0.371716i	$-0.878769\pi$
$431$	−38.5459	−1.85669	−0.928346	+	0.371716i	$0.878769\pi$
$432$	5.06697	0.243785
$433$	27.5890	1.32584	0.662922	−	0.748689i	$-0.269316\pi$
$433$	27.5890	1.32584	0.662922	+	0.748689i	$0.269316\pi$
$434$	−0.794988	−0.0381606
$435$	20.0856	0.963029
$436$	−33.1976	−1.58988
$437$	−0.133768	−0.00639897
$438$	1.50764	0.0720378
$439$	−18.5614	−0.885887	−0.442943	−	0.896550i	$-0.646066\pi$
$439$	−18.5614	−0.885887	−0.442943	+	0.896550i	$0.646066\pi$
$440$	15.6858	0.747793
$441$	2.42462	0.115458
$442$	−4.80094	−0.228358
$443$	4.02148	0.191066	0.0955332	−	0.995426i	$-0.469544\pi$
$443$	4.02148	0.191066	0.0955332	+	0.995426i	$0.469544\pi$
$444$	−42.5814	−2.02082
$445$	−9.92277	−0.470384
$446$	5.14008	0.243390
$447$	5.47149	0.258793
$448$	7.13223	0.336966
$449$	−25.0013	−1.17989	−0.589943	−	0.807445i	$-0.700850\pi$
$449$	−25.0013	−1.17989	−0.589943	+	0.807445i	$0.700850\pi$
$450$	4.82206	0.227314
$451$	49.9475	2.35194
$452$	−10.9667	−0.515829
$453$	7.98647	0.375237
$454$	3.50312	0.164410
$455$	−23.8298	−1.11716
$456$	0.0661669	0.00309855
$457$	−10.2474	−0.479354	−0.239677	−	0.970853i	$-0.577042\pi$
$457$	−10.2474	−0.479354	−0.239677	+	0.970853i	$0.577042\pi$
$458$	0.818826	0.0382612
$459$	−5.52552	−0.257909
$460$	27.5315	1.28366
$461$	10.5197	0.489951	0.244975	−	0.969529i	$-0.421220\pi$
$461$	10.5197	0.489951	0.244975	+	0.969529i	$0.421220\pi$
$462$	−2.35057	−0.109358
$463$	25.2692	1.17436	0.587179	−	0.809457i	$-0.300238\pi$
$463$	25.2692	1.17436	0.587179	+	0.809457i	$0.300238\pi$
$464$	−8.31471	−0.386001
$465$	−37.8945	−1.75732
$466$	−0.188175	−0.00871705
$467$	4.08966	0.189247	0.0946234	−	0.995513i	$-0.469835\pi$
$467$	4.08966	0.189247	0.0946234	+	0.995513i	$0.469835\pi$
$468$	−28.9257	−1.33709
$469$	−4.40596	−0.203448
$470$	−2.90932	−0.134197
$471$	46.3364	2.13507
$472$	7.52694	0.346455
$473$	60.2229	2.76905
$474$	−4.34392	−0.199523
$475$	0.388260	0.0178146
$476$	−8.09505	−0.371036
$477$	−24.1869	−1.10744
$478$	−1.70294	−0.0778908
$479$	−36.7606	−1.67963	−0.839817	−	0.542869i	$-0.817338\pi$
$479$	−36.7606	−1.67963	−0.839817	+	0.542869i	$0.817338\pi$
$480$	−20.4904	−0.935254
$481$	−56.5859	−2.58010
$482$	−5.26309	−0.239727
$483$	−8.32853	−0.378961
$484$	−32.8660	−1.49391
$485$	−22.9544	−1.04230
$486$	3.86887	0.175495
$487$	−33.7554	−1.52960	−0.764802	−	0.644265i	$-0.777163\pi$
$487$	−33.7554	−1.52960	−0.764802	+	0.644265i	$0.777163\pi$
$488$	0.290113	0.0131328
$489$	−15.5695	−0.704076
$490$	0.751445	0.0339468
$491$	2.85086	0.128657	0.0643286	−	0.997929i	$-0.479509\pi$
$491$	2.85086	0.128657	0.0643286	+	0.997929i	$0.479509\pi$
$492$	−43.3637	−1.95499
$493$	9.06718	0.408365
$494$	0.0435569	0.00195972
$495$	−50.0800	−2.25093
$496$	15.6870	0.704366
$497$	10.3123	0.462572
$498$	−7.37525	−0.330493
$499$	−14.9560	−0.669524	−0.334762	−	0.942303i	$-0.608656\pi$
$499$	−14.9560	−0.669524	−0.334762	+	0.942303i	$0.608656\pi$
$500$	−41.4141	−1.85209
$501$	−37.3296	−1.66776
$502$	−1.46753	−0.0654992
$503$	−8.56487	−0.381889	−0.190944	−	0.981601i	$-0.561155\pi$
$503$	−8.56487	−0.381889	−0.190944	+	0.981601i	$0.561155\pi$
$504$	1.84133	0.0820195
$505$	−6.99661	−0.311345
$506$	3.60888	0.160434
$507$	−55.7219	−2.47470
$508$	1.96328	0.0871066
$509$	24.3428	1.07898	0.539489	−	0.841993i	$-0.318618\pi$
$509$	24.3428	1.07898	0.539489	+	0.841993i	$0.318618\pi$
$510$	7.21637	0.319546
$511$	3.37816	0.149441
$512$	14.2252	0.628670
$513$	0.0501307	0.00221333
$514$	−3.70692	−0.163505
$515$	−32.0418	−1.41193
$516$	−52.2846	−2.30170
$517$	20.3916	0.896820
$518$	1.78437	0.0784007
$519$	34.6061	1.51904
$520$	−18.0971	−0.793610
$521$	−33.9526	−1.48749	−0.743745	−	0.668464i	$-0.766952\pi$
$521$	−33.9526	−1.48749	−0.743745	+	0.668464i	$0.766952\pi$
$522$	−1.02167	−0.0447175
$523$	33.7243	1.47466	0.737331	−	0.675532i	$-0.236086\pi$
$523$	33.7243	1.47466	0.737331	+	0.675532i	$0.236086\pi$
$524$	30.8245	1.34657
$525$	24.1735	1.05502
$526$	2.44144	0.106452
$527$	−17.1066	−0.745176
$528$	46.3823	2.01853
$529$	−10.2131	−0.444046
$530$	−7.49605	−0.325608
$531$	−24.0312	−1.04286
$532$	0.0734430	0.00318416
$533$	−57.6255	−2.49604
$534$	1.12924	0.0488670
$535$	12.6573	0.547221
$536$	−3.34602	−0.144526
$537$	24.2263	1.04544
$538$	1.73022	0.0745951
$539$	−5.26691	−0.226862
$540$	−10.3177	−0.444004
$541$	−22.8612	−0.982879	−0.491439	−	0.870912i	$-0.663529\pi$
$541$	−22.8612	−0.982879	−0.491439	+	0.870912i	$0.663529\pi$
$542$	3.18171	0.136666
$543$	14.2263	0.610508
$544$	−9.24992	−0.396587
$545$	66.3113	2.84046
$546$	2.71191	0.116059
$547$	−30.4179	−1.30058	−0.650288	−	0.759688i	$-0.725352\pi$
$547$	−30.4179	−1.30058	−0.650288	+	0.759688i	$0.725352\pi$
$548$	−15.6555	−0.668770
$549$	−0.926239	−0.0395309
$550$	−10.4748	−0.446645
$551$	−0.0822627	−0.00350451
$552$	−6.32494	−0.269207
$553$	−9.73339	−0.413906
$554$	−1.49291	−0.0634275
$555$	85.0551	3.61039
$556$	6.69230	0.283817
$557$	24.3671	1.03247	0.516233	−	0.856448i	$-0.327334\pi$
$557$	24.3671	1.03247	0.516233	+	0.856448i	$0.327334\pi$
$558$	1.92755	0.0815995
$559$	−69.4804	−2.93871
$560$	−14.8278	−0.626588
$561$	−50.5798	−2.13548
$562$	−1.71428	−0.0723127
$563$	−39.1345	−1.64932	−0.824661	−	0.565627i	$-0.808634\pi$
$563$	−39.1345	−1.64932	−0.824661	+	0.565627i	$0.808634\pi$
$564$	−17.7036	−0.745458
$565$	21.9056	0.921577
$566$	−2.20565	−0.0927103
$567$	10.3951	0.436552
$568$	7.83151	0.328603
$569$	41.9315	1.75786	0.878930	−	0.476951i	$-0.158258\pi$
$569$	41.9315	1.75786	0.878930	+	0.476951i	$0.158258\pi$
$570$	−0.0654711	−0.00274228
$571$	1.63409	0.0683845	0.0341923	−	0.999415i	$-0.489114\pi$
$571$	1.63409	0.0683845	0.0341923	+	0.999415i	$0.489114\pi$
$572$	62.8341	2.62723
$573$	−20.2151	−0.844499
$574$	1.81715	0.0758464
$575$	−37.1141	−1.54776
$576$	−17.2930	−0.720540
$577$	−3.28569	−0.136785	−0.0683925	−	0.997658i	$-0.521787\pi$
$577$	−3.28569	−0.136785	−0.0683925	+	0.997658i	$0.521787\pi$
$578$	0.000185428 0	7.71277e−6 0
$579$	9.97867	0.414700
$580$	16.9310	0.703021
$581$	−16.5257	−0.685600
$582$	2.61228	0.108282
$583$	52.5402	2.17599
$584$	2.56547	0.106160
$585$	57.7784	2.38884
$586$	−0.845997	−0.0349478
$587$	−37.3079	−1.53986	−0.769931	−	0.638127i	$-0.779709\pi$
$587$	−37.3079	−1.53986	−0.769931	+	0.638127i	$0.779709\pi$
$588$	4.57265	0.188573
$589$	0.155201	0.00639495
$590$	−7.44779	−0.306621
$591$	−48.6173	−1.99985
$592$	−35.2098	−1.44711
$593$	−10.6325	−0.436626	−0.218313	−	0.975879i	$-0.570055\pi$
$593$	−10.6325	−0.436626	−0.218313	+	0.975879i	$0.570055\pi$
$594$	−1.35246	−0.0554922
$595$	16.1697	0.662891
$596$	4.61215	0.188921
$597$	−54.3122	−2.22285
$598$	−4.16364	−0.170264
$599$	42.0174	1.71678	0.858391	−	0.512995i	$-0.171464\pi$
$599$	42.0174	1.71678	0.858391	+	0.512995i	$0.171464\pi$
$600$	18.3581	0.749467
$601$	−16.1101	−0.657144	−0.328572	−	0.944479i	$-0.606567\pi$
$601$	−16.1101	−0.657144	−0.328572	+	0.944479i	$0.606567\pi$
$602$	2.19098	0.0892977
$603$	10.6828	0.435037
$604$	6.73214	0.273927
$605$	65.6489	2.66901
$606$	0.796236	0.0323449
$607$	−14.1660	−0.574979	−0.287489	−	0.957784i	$-0.592821\pi$
$607$	−14.1660	−0.574979	−0.287489	+	0.957784i	$0.592821\pi$
$608$	0.0839207	0.00340343
$609$	−5.12177	−0.207545
$610$	−0.287062	−0.0116228
$611$	−23.5262	−0.951768
$612$	19.6275	0.793393
$613$	17.1420	0.692361	0.346180	−	0.938168i	$-0.387479\pi$
$613$	17.1420	0.692361	0.346180	+	0.938168i	$0.387479\pi$
$614$	0.925335	0.0373435
$615$	86.6178	3.49277
$616$	−3.99985	−0.161159
$617$	30.3241	1.22080	0.610401	−	0.792092i	$-0.291008\pi$
$617$	30.3241	1.22080	0.610401	+	0.792092i	$0.291008\pi$
$618$	3.64645	0.146682
$619$	−9.91575	−0.398547	−0.199274	−	0.979944i	$-0.563858\pi$
$619$	−9.91575	−0.398547	−0.199274	+	0.979944i	$0.563858\pi$
$620$	−31.9429	−1.28286
$621$	−4.79203	−0.192298
$622$	−3.02023	−0.121100
$623$	2.53028	0.101374
$624$	−53.5123	−2.14221
$625$	30.8286	1.23314
$626$	2.54033	0.101532
$627$	0.458890	0.0183263
$628$	39.0590	1.55862
$629$	38.3962	1.53096
$630$	−1.82197	−0.0725890
$631$	−4.94297	−0.196777	−0.0983884	−	0.995148i	$-0.531369\pi$
$631$	−4.94297	−0.196777	−0.0983884	+	0.995148i	$0.531369\pi$
$632$	−7.39183	−0.294031
$633$	40.2390	1.59936
$634$	0.994685	0.0395040
$635$	−3.92161	−0.155624
$636$	−45.6146	−1.80873
$637$	6.07655	0.240762
$638$	2.21934	0.0878645
$639$	−25.0035	−0.989125
$640$	−22.9547	−0.907365
$641$	8.92412	0.352481	0.176241	−	0.984347i	$-0.443606\pi$
$641$	8.92412	0.352481	0.176241	+	0.984347i	$0.443606\pi$
$642$	−1.44043	−0.0568494
$643$	8.44158	0.332903	0.166452	−	0.986050i	$-0.446769\pi$
$643$	8.44158	0.332903	0.166452	+	0.986050i	$0.446769\pi$
$644$	−7.02047	−0.276645
$645$	104.437	4.11220
$646$	−0.0295554	−0.00116284
$647$	50.2006	1.97359	0.986795	−	0.161976i	$-0.0517866\pi$
$647$	50.2006	1.97359	0.986795	+	0.161976i	$0.0517866\pi$
$648$	7.89433	0.310119
$649$	52.2019	2.04910
$650$	12.0850	0.474011
$651$	9.66301	0.378723
$652$	−13.1242	−0.513982
$653$	40.5316	1.58612	0.793062	−	0.609141i	$-0.208486\pi$
$653$	40.5316	1.58612	0.793062	+	0.609141i	$0.208486\pi$
$654$	−7.54643	−0.295089
$655$	−61.5711	−2.40578
$656$	−35.8567	−1.39997
$657$	−8.19076	−0.319552
$658$	0.741870	0.0289211
$659$	41.9115	1.63264	0.816320	−	0.577600i	$-0.196011\pi$
$659$	41.9115	1.63264	0.816320	+	0.577600i	$0.196011\pi$
$660$	−94.4468	−3.67634
$661$	27.5407	1.07121	0.535605	−	0.844469i	$-0.320084\pi$
$661$	27.5407	1.07121	0.535605	+	0.844469i	$0.320084\pi$
$662$	−2.14388	−0.0833242
$663$	58.3550	2.26632
$664$	−12.5501	−0.487038
$665$	−0.146700	−0.00568880
$666$	−4.32642	−0.167646
$667$	7.86355	0.304478
$668$	−31.4667	−1.21748
$669$	−62.4772	−2.41551
$670$	3.31083	0.127909
$671$	2.01203	0.0776735
$672$	5.22500	0.201559
$673$	6.81901	0.262853	0.131427	−	0.991326i	$-0.458044\pi$
$673$	6.81901	0.262853	0.131427	+	0.991326i	$0.458044\pi$
$674$	3.28623	0.126581
$675$	13.9089	0.535352
$676$	−46.9704	−1.80655
$677$	−6.66448	−0.256137	−0.128068	−	0.991765i	$-0.540878\pi$
$677$	−6.66448	−0.256137	−0.128068	+	0.991765i	$0.540878\pi$
$678$	−2.49293	−0.0957403
$679$	5.85331	0.224629
$680$	12.2797	0.470906
$681$	−42.5801	−1.63167
$682$	−4.18713	−0.160333
$683$	23.2496	0.889623	0.444811	−	0.895624i	$-0.353271\pi$
$683$	23.2496	0.889623	0.444811	+	0.895624i	$0.353271\pi$
$684$	−0.178072	−0.00680874
$685$	31.2715	1.19482
$686$	−0.191617	−0.00731595
$687$	−9.95276	−0.379722
$688$	−43.2332	−1.64825
$689$	−60.6167	−2.30931
$690$	6.25843	0.238254
$691$	7.85702	0.298895	0.149447	−	0.988770i	$-0.452251\pi$
$691$	7.85702	0.298895	0.149447	+	0.988770i	$0.452251\pi$
$692$	29.1710	1.10892
$693$	12.7703	0.485103
$694$	0.00492285	0.000186869 0
$695$	−13.3677	−0.507066
$696$	−3.88963	−0.147436
$697$	39.1016	1.48108
$698$	4.58881	0.173689
$699$	2.28725	0.0865119
$700$	20.3769	0.770175
$701$	−0.243911	−0.00921239	−0.00460619	−	0.999989i	$-0.501466\pi$
$701$	−0.243911	−0.00921239	−0.00460619	+	0.999989i	$0.501466\pi$
$702$	1.56036	0.0588922
$703$	−0.348353	−0.0131384
$704$	37.5648	1.41578
$705$	35.3626	1.33183
$706$	−1.21452	−0.0457092
$707$	1.78412	0.0670987
$708$	−45.3208	−1.70326
$709$	27.6428	1.03815	0.519073	−	0.854730i	$-0.326277\pi$
$709$	27.6428	1.03815	0.519073	+	0.854730i	$0.326277\pi$
$710$	−7.74915	−0.290820
$711$	23.5998	0.885062
$712$	1.92157	0.0720140
$713$	−14.8358	−0.555605
$714$	−1.84016	−0.0688661
$715$	−125.509	−4.69379
$716$	20.4214	0.763183
$717$	20.6991	0.773023
$718$	−2.10417	−0.0785269
$719$	13.2320	0.493470	0.246735	−	0.969083i	$-0.420642\pi$
$719$	13.2320	0.493470	0.246735	+	0.969083i	$0.420642\pi$
$720$	35.9518	1.33984
$721$	8.17058	0.304288
$722$	−3.64045	−0.135483
$723$	63.9724	2.37916
$724$	11.9919	0.445677
$725$	−22.8239	−0.847660
$726$	−7.47105	−0.277277
$727$	−19.0077	−0.704958	−0.352479	−	0.935820i	$-0.614661\pi$
$727$	−19.0077	−0.704958	−0.352479	+	0.935820i	$0.614661\pi$
$728$	4.61471	0.171033
$729$	−15.8405	−0.586687
$730$	−2.53850	−0.0939540
$731$	47.1458	1.74375
$732$	−1.74681	−0.0645640
$733$	−49.8815	−1.84242	−0.921208	−	0.389071i	$-0.872796\pi$
$733$	−49.8815	−1.84242	−0.921208	+	0.389071i	$0.872796\pi$
$734$	4.03676	0.148999
$735$	−9.13374	−0.336903
$736$	−8.02204	−0.295696
$737$	−23.2058	−0.854796
$738$	−4.40591	−0.162184
$739$	−29.8966	−1.09976	−0.549882	−	0.835242i	$-0.685327\pi$
$739$	−29.8966	−1.09976	−0.549882	+	0.835242i	$0.685327\pi$
$740$	71.6966	2.63562
$741$	−0.529431	−0.0194491
$742$	1.91148	0.0701725
$743$	7.33058	0.268933	0.134467	−	0.990918i	$-0.457068\pi$
$743$	7.33058	0.268933	0.134467	+	0.990918i	$0.457068\pi$
$744$	7.33838	0.269038
$745$	−9.21265	−0.337525
$746$	2.03174	0.0743871
$747$	40.0685	1.46603
$748$	−42.6359	−1.55892
$749$	−3.22757	−0.117933
$750$	−9.41419	−0.343758
$751$	−37.8737	−1.38203	−0.691015	−	0.722840i	$-0.742836\pi$
$751$	−37.8737	−1.38203	−0.691015	+	0.722840i	$0.742836\pi$
$752$	−14.6389	−0.533824
$753$	17.8377	0.650043
$754$	−2.56050	−0.0932480
$755$	−13.4473	−0.489396
$756$	2.63099	0.0956882
$757$	22.7557	0.827070	0.413535	−	0.910488i	$-0.364294\pi$
$757$	22.7557	0.827070	0.413535	+	0.910488i	$0.364294\pi$
$758$	−1.06860	−0.0388135
$759$	−43.8656	−1.59222
$760$	−0.111409	−0.00404122
$761$	7.34081	0.266104	0.133052	−	0.991109i	$-0.457522\pi$
$761$	7.34081	0.266104	0.133052	+	0.991109i	$0.457522\pi$
$762$	0.446291	0.0161674
$763$	−16.9092	−0.612155
$764$	−17.0402	−0.616493
$765$	−39.2053	−1.41747
$766$	3.78145	0.136629
$767$	−60.2264	−2.17465
$768$	−30.6108	−1.10457
$769$	−39.6967	−1.43150	−0.715749	−	0.698358i	$-0.753915\pi$
$769$	−39.6967	−1.43150	−0.715749	+	0.698358i	$0.753915\pi$
$770$	3.95779	0.142629
$771$	45.0573	1.62270
$772$	8.41145	0.302735
$773$	−9.92476	−0.356969	−0.178484	−	0.983943i	$-0.557119\pi$
$773$	−9.92476	−0.356969	−0.178484	+	0.983943i	$0.557119\pi$
$774$	−5.31231	−0.190947
$775$	43.0609	1.54679
$776$	4.44518	0.159573
$777$	−21.6889	−0.778083
$778$	3.08690	0.110671
$779$	−0.354753	−0.0127103
$780$	108.965	3.90159
$781$	54.3141	1.94351
$782$	2.82523	0.101030
$783$	−2.94694	−0.105315
$784$	3.78105	0.135037
$785$	−78.0193	−2.78463
$786$	7.00698	0.249931
$787$	17.2831	0.616077	0.308038	−	0.951374i	$-0.400327\pi$
$787$	17.2831	0.616077	0.308038	+	0.951374i	$0.400327\pi$
$788$	−40.9816	−1.45991
$789$	−29.6754	−1.05647
$790$	7.31410	0.260224
$791$	−5.58588	−0.198611
$792$	9.69814	0.344608
$793$	−2.32132	−0.0824325
$794$	−1.30426	−0.0462865
$795$	91.1139	3.23148
$796$	−45.7821	−1.62270
$797$	3.27024	0.115838	0.0579190	−	0.998321i	$-0.481553\pi$
$797$	3.27024	0.115838	0.0579190	+	0.998321i	$0.481553\pi$
$798$	0.0166950	0.000590995 0
$799$	15.9636	0.564753
$800$	23.2839	0.823212
$801$	−6.13498	−0.216769
$802$	−3.29560	−0.116372
$803$	17.7924	0.627881
$804$	20.1469	0.710526
$805$	14.0232	0.494253
$806$	4.83078	0.170157
$807$	−21.0307	−0.740315
$808$	1.35491	0.0476657
$809$	−45.7392	−1.60810	−0.804052	−	0.594558i	$-0.797327\pi$
$809$	−45.7392	−1.60810	−0.804052	+	0.594558i	$0.797327\pi$
$810$	−7.81132	−0.274462
$811$	20.1033	0.705923	0.352962	−	0.935638i	$-0.385175\pi$
$811$	20.1033	0.705923	0.352962	+	0.935638i	$0.385175\pi$
$812$	−4.31736	−0.151510
$813$	−38.6734	−1.35633
$814$	9.39811	0.329403
$815$	26.2152	0.918278
$816$	36.3106	1.27113
$817$	−0.427734	−0.0149645
$818$	0.599886	0.0209745
$819$	−14.7333	−0.514825
$820$	73.0138	2.54975
$821$	−19.1738	−0.669170	−0.334585	−	0.942366i	$-0.608596\pi$
$821$	−19.1738	−0.669170	−0.334585	+	0.942366i	$0.608596\pi$
$822$	−3.55879	−0.124127
$823$	8.70002	0.303264	0.151632	−	0.988437i	$-0.451547\pi$
$823$	8.70002	0.303264	0.151632	+	0.988437i	$0.451547\pi$
$824$	6.20499	0.216161
$825$	127.320	4.43271
$826$	1.89917	0.0660805
$827$	11.0112	0.382898	0.191449	−	0.981503i	$-0.438681\pi$
$827$	11.0112	0.382898	0.191449	+	0.981503i	$0.438681\pi$
$828$	17.0220	0.591556
$829$	40.0764	1.39191	0.695955	−	0.718086i	$-0.254981\pi$
$829$	40.0764	1.39191	0.695955	+	0.718086i	$0.254981\pi$
$830$	12.4181	0.431039
$831$	18.1462	0.629483
$832$	−43.3393	−1.50252
$833$	−4.12322	−0.142861
$834$	1.52128	0.0526778
$835$	62.8539	2.17515
$836$	0.386818	0.0133784
$837$	5.55986	0.192177
$838$	3.61077	0.124732
$839$	−5.37182	−0.185456	−0.0927279	−	0.995691i	$-0.529559\pi$
$839$	−5.37182	−0.185456	−0.0927279	+	0.995691i	$0.529559\pi$
$840$	−6.93644	−0.239330
$841$	−24.1642	−0.833247
$842$	−2.52036	−0.0868574
$843$	20.8370	0.717664
$844$	33.9192	1.16755
$845$	93.8221	3.22758
$846$	−1.79876	−0.0618425
$847$	−16.7403	−0.575204
$848$	−37.7179	−1.29524
$849$	26.8095	0.920099
$850$	−8.20021	−0.281265
$851$	33.2993	1.14149
$852$	−47.1547	−1.61549
$853$	37.5087	1.28427	0.642137	−	0.766590i	$-0.278048\pi$
$853$	37.5087	1.28427	0.642137	+	0.766590i	$0.278048\pi$
$854$	0.0732001	0.00250485
$855$	0.355694	0.0121645
$856$	−2.45111	−0.0837774
$857$	17.2234	0.588339	0.294169	−	0.955753i	$-0.404957\pi$
$857$	17.2234	0.588339	0.294169	+	0.955753i	$0.404957\pi$
$858$	14.2834	0.487626
$859$	−26.0045	−0.887262	−0.443631	−	0.896210i	$-0.646310\pi$
$859$	−26.0045	−0.887262	−0.443631	+	0.896210i	$0.646310\pi$
$860$	88.0345	3.00195
$861$	−22.0873	−0.752734
$862$	−7.38604	−0.251569
$863$	32.4210	1.10362	0.551812	−	0.833969i	$-0.313937\pi$
$863$	32.4210	1.10362	0.551812	+	0.833969i	$0.313937\pi$
$864$	3.00634	0.102278
$865$	−58.2683	−1.98118
$866$	5.28651	0.179643
$867$	−0.00225386	−7.65450e−5 0
$868$	8.14536	0.276472
$869$	−51.2649	−1.73904
$870$	3.84873	0.130484
$871$	26.7730	0.907169
$872$	−12.8414	−0.434864
$873$	−14.1921	−0.480329
$874$	−0.0256321	−0.000867018 0
$875$	−21.0943	−0.713117
$876$	−15.4471	−0.521910
$877$	31.8805	1.07653	0.538264	−	0.842776i	$-0.319080\pi$
$877$	31.8805	1.07653	0.538264	+	0.842776i	$0.319080\pi$
$878$	−3.55667	−0.120032
$879$	10.2830	0.346838
$880$	−78.0965	−2.63263
$881$	−10.9692	−0.369563	−0.184782	−	0.982780i	$-0.559158\pi$
$881$	−10.9692	−0.369563	−0.184782	+	0.982780i	$0.559158\pi$
$882$	0.464598	0.0156438
$883$	−43.5368	−1.46513	−0.732564	−	0.680698i	$-0.761677\pi$
$883$	−43.5368	−1.46513	−0.732564	+	0.680698i	$0.761677\pi$
$884$	49.1900	1.65444
$885$	90.5272	3.04304
$886$	0.770582	0.0258882
$887$	−12.9767	−0.435715	−0.217857	−	0.975981i	$-0.569907\pi$
$887$	−12.9767	−0.435715	−0.217857	+	0.975981i	$0.569907\pi$
$888$	−16.4712	−0.552736
$889$	1.00000	0.0335389
$890$	−1.90137	−0.0637339
$891$	54.7499	1.83419
$892$	−52.6647	−1.76335
$893$	−0.144831	−0.00484660
$894$	1.04843	0.0350647
$895$	−40.7912	−1.36350
$896$	5.85340	0.195548
$897$	50.6087	1.68977
$898$	−4.79067	−0.159867
$899$	−9.12353	−0.304287
$900$	−49.4063	−1.64688
$901$	41.1313	1.37028
$902$	9.57077	0.318672
$903$	−26.6312	−0.886231
$904$	−4.24209	−0.141090
$905$	−23.9536	−0.796243
$906$	1.53034	0.0508421
$907$	−2.23113	−0.0740833	−0.0370417	−	0.999314i	$-0.511793\pi$
$907$	−2.23113	−0.0740833	−0.0370417	+	0.999314i	$0.511793\pi$
$908$	−35.8926	−1.19114
$909$	−4.32582	−0.143478
$910$	−4.56619	−0.151368
$911$	29.4118	0.974457	0.487228	−	0.873275i	$-0.338008\pi$
$911$	29.4118	0.974457	0.487228	+	0.873275i	$0.338008\pi$
$912$	−0.329431	−0.0109086
$913$	−87.0391	−2.88058
$914$	−1.96358	−0.0649493
$915$	3.48921	0.115350
$916$	−8.38961	−0.277201
$917$	15.7005	0.518476
$918$	−1.05878	−0.0349450
$919$	3.92759	0.129559	0.0647796	−	0.997900i	$-0.479366\pi$
$919$	3.92759	0.129559	0.0647796	+	0.997900i	$0.479366\pi$
$920$	10.6497	0.351109
$921$	−11.2474	−0.370613
$922$	2.01575	0.0663851
$923$	−62.6634	−2.06259
$924$	24.0837	0.792296
$925$	−96.6511	−3.17787
$926$	4.84199	0.159118
$927$	−19.8106	−0.650665
$928$	−4.93329	−0.161943
$929$	26.5871	0.872293	0.436147	−	0.899876i	$-0.356343\pi$
$929$	26.5871	0.872293	0.436147	+	0.899876i	$0.356343\pi$
$930$	−7.26121	−0.238105
$931$	0.0374083	0.00122601
$932$	1.92802	0.0631546
$933$	36.7106	1.20185
$934$	0.783646	0.0256417
$935$	85.1641	2.78516
$936$	−11.1889	−0.365722
$937$	−46.5758	−1.52156	−0.760782	−	0.649007i	$-0.775185\pi$
$937$	−46.5758	−1.52156	−0.760782	+	0.649007i	$0.775185\pi$
$938$	−0.844254	−0.0275659
$939$	−30.8774	−1.00765
$940$	29.8086	0.972250
$941$	−3.71923	−0.121243	−0.0606217	−	0.998161i	$-0.519308\pi$
$941$	−3.71923	−0.121243	−0.0606217	+	0.998161i	$0.519308\pi$
$942$	8.87883	0.289288
$943$	33.9111	1.10430
$944$	−37.4751	−1.21971
$945$	−5.25533	−0.170956
$946$	11.5397	0.375188
$947$	−1.23688	−0.0401934	−0.0200967	−	0.999798i	$-0.506397\pi$
$947$	−1.23688	−0.0401934	−0.0200967	+	0.999798i	$0.506397\pi$
$948$	44.5074	1.44553
$949$	−20.5275	−0.666351
$950$	0.0743971	0.00241376
$951$	−12.0903	−0.392055
$952$	−3.13130	−0.101486
$953$	−52.2025	−1.69101	−0.845503	−	0.533971i	$-0.820699\pi$
$953$	−52.2025	−1.69101	−0.845503	+	0.533971i	$0.820699\pi$
$954$	−4.63461	−0.150051
$955$	34.0373	1.10142
$956$	17.4482	0.564314
$957$	−26.9759	−0.872007
$958$	−7.04394	−0.227579
$959$	−7.97414	−0.257499
$960$	65.1439	2.10251
$961$	−13.7871	−0.444744
$962$	−10.8428	−0.349586
$963$	7.82564	0.252178
$964$	53.9251	1.73681
$965$	−16.8017	−0.540864
$966$	−1.59588	−0.0513467
$967$	25.3043	0.813731	0.406866	−	0.913488i	$-0.366622\pi$
$967$	25.3043	0.813731	0.406866	+	0.913488i	$0.366622\pi$
$968$	−12.7131	−0.408615
$969$	0.359244	0.0115406
$970$	−4.39844	−0.141225
$971$	4.96055	0.159192	0.0795958	−	0.996827i	$-0.474637\pi$
$971$	4.96055	0.159192	0.0795958	+	0.996827i	$0.474637\pi$
$972$	−39.6400	−1.27145
$973$	3.40873	0.109279
$974$	−6.46810	−0.207251
$975$	−146.892	−4.70430
$976$	−1.44441	−0.0462344
$977$	−3.61365	−0.115611	−0.0578055	−	0.998328i	$-0.518410\pi$
$977$	−3.61365	−0.115611	−0.0578055	+	0.998328i	$0.518410\pi$
$978$	−2.98337	−0.0953976
$979$	13.3268	0.425925
$980$	−7.69922	−0.245943
$981$	40.9985	1.30898
$982$	0.546271	0.0174322
$983$	−51.8644	−1.65422	−0.827109	−	0.562042i	$-0.810016\pi$
$983$	−51.8644	−1.65422	−0.827109	+	0.562042i	$0.810016\pi$
$984$	−16.7738	−0.534729
$985$	81.8597	2.60827
$986$	1.73742	0.0553308
$987$	−9.01737	−0.287026
$988$	−0.446280	−0.0141981
$989$	40.8874	1.30014
$990$	−9.59615	−0.304986
$991$	6.60298	0.209751	0.104875	−	0.994485i	$-0.466556\pi$
$991$	6.60298	0.209751	0.104875	+	0.994485i	$0.466556\pi$
$992$	9.30741	0.295511
$993$	26.0587	0.826947
$994$	1.97601	0.0626754
$995$	91.4485	2.89911
$996$	75.5660	2.39440
$997$	−0.888839	−0.0281498	−0.0140749	−	0.999901i	$-0.504480\pi$
$997$	−0.888839	−0.0281498	−0.0140749	+	0.999901i	$0.504480\pi$
$998$	−2.86582	−0.0907160
$999$	−12.4792	−0.394826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	889.2.a.c.1.10	✓	16
3.2	odd	2		8001.2.a.t.1.7		16
7.6	odd	2		6223.2.a.k.1.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.c.1.10	✓	16	1.1	even	1	trivial
6223.2.a.k.1.10		16	7.6	odd	2
8001.2.a.t.1.7		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.a (trivial)

\(f(q)\)	\(=\)	\(q+0.191617 q^{2} -2.32908 q^{3} -1.96328 q^{4} +3.92161 q^{5} -0.446291 q^{6} -1.00000 q^{7} -0.759431 q^{8} +2.42462 q^{9} +0.751445 q^{10} -5.26691 q^{11} +4.57265 q^{12} +6.07655 q^{13} -0.191617 q^{14} -9.13374 q^{15} +3.78105 q^{16} -4.12322 q^{17} +0.464598 q^{18} +0.0374083 q^{19} -7.69922 q^{20} +2.32908 q^{21} -1.00923 q^{22} -3.57588 q^{23} +1.76878 q^{24} +10.3790 q^{25} +1.16437 q^{26} +1.34010 q^{27} +1.96328 q^{28} -2.19905 q^{29} -1.75018 q^{30} +4.14885 q^{31} +2.24337 q^{32} +12.2671 q^{33} -0.790078 q^{34} -3.92161 q^{35} -4.76022 q^{36} -9.31219 q^{37} +0.00716804 q^{38} -14.1528 q^{39} -2.97819 q^{40} -9.48327 q^{41} +0.446291 q^{42} -11.4342 q^{43} +10.3404 q^{44} +9.50842 q^{45} -0.685199 q^{46} -3.87164 q^{47} -8.80637 q^{48} +1.00000 q^{49} +1.98879 q^{50} +9.60333 q^{51} -11.9300 q^{52} -9.97552 q^{53} +0.256785 q^{54} -20.6547 q^{55} +0.759431 q^{56} -0.0871269 q^{57} -0.421374 q^{58} -9.91129 q^{59} +17.9321 q^{60} -0.382013 q^{61} +0.794988 q^{62} -2.42462 q^{63} -7.13223 q^{64} +23.8298 q^{65} +2.35057 q^{66} +4.40596 q^{67} +8.09505 q^{68} +8.32853 q^{69} -0.751445 q^{70} -10.3123 q^{71} -1.84133 q^{72} -3.37816 q^{73} -1.78437 q^{74} -24.1735 q^{75} -0.0734430 q^{76} +5.26691 q^{77} -2.71191 q^{78} +9.73339 q^{79} +14.8278 q^{80} -10.3951 q^{81} -1.81715 q^{82} +16.5257 q^{83} -4.57265 q^{84} -16.1697 q^{85} -2.19098 q^{86} +5.12177 q^{87} +3.99985 q^{88} -2.53028 q^{89} +1.82197 q^{90} -6.07655 q^{91} +7.02047 q^{92} -9.66301 q^{93} -0.741870 q^{94} +0.146700 q^{95} -5.22500 q^{96} -5.85331 q^{97} +0.191617 q^{98} -12.7703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{3} + 12 q^{4} - 9 q^{5} - 12 q^{6} - 16 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} - 22 q^{11} - 10 q^{12} - 4 q^{13} + 2 q^{14} - 14 q^{15} + 12 q^{16} - 18 q^{17} - 5 q^{18} - 15 q^{19}+ \cdots - 73 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^3 + 12 * q^4 - 9 * q^5 - 12 * q^6 - 16 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 - 22 * q^11 - 10 * q^12 - 4 * q^13 + 2 * q^14 - 14 * q^15 + 12 * q^16 - 18 * q^17 - 5 * q^18 - 15 * q^19 - 40 * q^20 + 4 * q^21 - 11 * q^22 - 5 * q^23 - 26 * q^24 + 15 * q^25 - 24 * q^26 - 10 * q^27 - 12 * q^28 - 12 * q^29 + 3 * q^30 - 32 * q^31 - 9 * q^32 - 10 * q^33 - 14 * q^34 + 9 * q^35 + 10 * q^36 - 2 * q^37 + 3 * q^38 - 41 * q^39 - 14 * q^40 - 45 * q^41 + 12 * q^42 - 3 * q^43 - 54 * q^44 - 22 * q^45 - 49 * q^47 + 10 * q^48 + 16 * q^49 - 6 * q^50 - 12 * q^51 + 38 * q^52 + 16 * q^53 - 67 * q^54 + 7 * q^55 + 6 * q^56 + 8 * q^57 + 16 * q^58 - 35 * q^59 + 56 * q^60 - 11 * q^61 + 17 * q^62 - 14 * q^63 - 2 * q^64 + 14 * q^65 + 86 * q^66 + 17 * q^67 - 71 * q^68 - 17 * q^69 + 2 * q^70 - 81 * q^71 + 13 * q^72 - 15 * q^73 + 13 * q^74 - 48 * q^75 + 14 * q^76 + 22 * q^77 - 10 * q^78 - 34 * q^79 - 33 * q^80 + 40 * q^81 - 14 * q^82 - 39 * q^83 + 10 * q^84 - 17 * q^85 + 36 * q^86 + 7 * q^87 + 61 * q^88 - 32 * q^89 + 79 * q^90 + 4 * q^91 + 37 * q^92 + 27 * q^93 + 13 * q^94 - 33 * q^95 - 55 * q^96 - 4 * q^97 - 2 * q^98 - 73 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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